Intermittent contact imaging under force-feedback control

ABSTRACT

An interfacial force microscope includes a differential-capacitance displacement sensor having a tip mounted on an oscillating member. The sensor generates displacement signals in response to oscillations of the member. A scanner is adjacent the sensor and supports a sample to be imaged. The scanner is actuable to move the sample relative to the sensor to bring the tip into intermittent contact with said sample as the member oscillates. A controller is in communication with the sensor and the scanner. The controller includes a sensor feedback circuit receiving the displacement signals and an AC setpoint signal. The AC setpoint signal has a frequency generally equal to the frequency at the peak of the displacement versus frequency curve of the sensor. The output of the sensor feedback circuit is applied to the sensor to oscillate the member. The controller also provides output to the scanner in response to the displacement signals to control the separation distance between the sensor and the sample.

FIELD OF THE INVENTION

[0001] The present invention relates generally to imaging and inparticular to a method and apparatus for intermittent contact imaging.

BACKGROUND OF THE INVENTION

[0002] Atomic-force microscopy has become widely used to image surfacesof samples on a microscopic scale. Its popularity to a large extent isdue to the fact that an atomic-force microscope (AFM) measures the forceor force gradient between a sharp tip disposed on a cantilever and asample surface at a picoNewton (pN) level as opposed to the tunnelingcurrent measured with a scanning tunneling microscope (STM). This ofcourse allows the AFM to image insulating as well as conducting samples.

[0003] AFMs can be operated in either contact or intermittent contactmodes. When operating in a contact mode, the deflection of a weakcantilever is kept constant while servoing the vertical extension of apiezoelectric scanner supporting the sample being imaged. Thepiezoelectric scanner is also rastered in an x-y plane to scan thesurface of the sample. A map of the vertical extension of thepiezoelectric scanner at various x,y coordinates of the sample surface,which is assumed to be proportional to a change in voltage on thepiezoelectric scanner, reflects the topography of the sample surface.Unfortunately, problems exist in that soft samples are often damaged bythe plowing action of the tip on the sample as the sample is rastered bythe piezoelectric scanner in the x-y plane.

[0004] When operating in an intermittent contact mode, the base of astiff cantilever is driven by a piezoelectric element which induces anoscillation at the free end of the cantilever. By driving the cantilevernear its resonant frequency, an oscillation amplitude ranging from 20 to100 nm at the free end of the cantilever can be achieved. This amplituderange is sufficient to inhibit the tip from sticking to the samplesurface during each contact. To generate the image, the verticalextension of the piezoelectric scanner is servoed to maintain a constantdrop in the oscillation amplitude. The piezoelectric scanner is alsorastered in an x-y plane to scan the surface of the sample. In order toachieve high sensitivity, a high quality factor (Q) is necessary.Tapping mode cantilevers typically have Q values ranging from 100 to1000 in air.

[0005] To enhance the measurement of force displacement curves, amodified form of atomic-force microscopy, referred to as interfacialforce microscopy, has been developed. Interfacial force microscopes(IFMs) replace the cantilever with a differential-capacitancedisplacement sensor. Feedback is used to servo the net electrostatictorque of the sensor such that it cancels the torque resulting fromtip-sample forces. As a consequence, the tip support remains at its restposition throughout the force profile. This feature eliminates thesnap-to-contact instability which plagues weak cantilevers in theattractive force regime and correlates the tip-sample deformationdirectly to the vertical extension of the piezoelectric scanner innanoindentation studies.

[0006] Feedback attempts to inhibit the common plate of the displacementsensor from actually deflecting which leads to rapid restabilization ofthe displacement sensor after hard collisions with pronounced surfacefeatures. However, this places considerable demands on the rate at whichforce signals drift since it is often necessary to image a large fieldof view at a slow lateral scan. Generally, a contact force in the rangeof 200 nN corresponds to a force signal in the order of 10 mV. As willbe appreciated, the force signal has very little room to drift over thescan duration. A slow drift in the attractive force direction results ina slight increase in the contact force applied to the sample over thescan. Drifts in the repulsive force direction can pull the piezoelectricscanner completely out of feedback. Accordingly, improved imagingtechniques are desired.

[0007] It is therefore an object of the present invention to provide anovel method and apparatus for intermittent imaging.

SUMMARY OF THE INVENTION

[0008] According to one aspect of the present invention there isprovided an apparatus for intermittent contact imaging comprising:

[0009] a sensor to contact intermittently a sample to be imaged andgenerating displacement signals during oscillation thereof;

[0010] a scanner adjacent said sensor and supporting said sample to beimaged, said scanner being actuable to move said sample relative to saidsensor to bring said sensor into intermittent contact with said sample;and

[0011] a controller in communication with said sensor and said scanner,said controller including a sensor feedback circuit receiving saiddisplacement signals and an AC setpoint signal, said AC setpoint signalhaving a frequency generally equal to the frequency at the peak of thedisplacement versus frequency curve of said sensor, the output of saidsensor feedback circuit being applied to said sensor to oscillate thesame, said controller further providing output to said scanner inresponse to said displacement signals to control the separation distancebetween said sensor and said sample.

[0012] According to another aspect of the present invention there isprovided an interfacial force microscope comprising:

[0013] a differential-capacitance displacement sensor having a tipmounted on an oscillating member, said sensor generating displacementsignals during oscillation of said member;

[0014] a scanner adjacent said sensor and supporting a sample to beimaged, said scanner being actuable to move said sample relative to saidsensor to bring said tip into intermittent contact with said sample andto move said sample relative to said sensor to raster said sensor oversaid sample; and

[0015] a controller in communication with said sensor and said scanner,said controller including a sensor feedback circuit receiving saiddisplacement signals and an AC setpoint signal, said AC setpoint signalhaving a frequency generally equal to the frequency at the peak of thedisplacement versus frequency curve of said sensor, the output of saidsensor feedback circuit being applied to said sensor to oscillate saidmember, said controller further providing output to said scanner inresponse to said displacement signals to control the separation distancebetween said sensor and said sample.

[0016] According to still yet another aspect of the present inventionthere is provided a method of imaging a sample surface comprising thesteps of:

[0017] oscillating a sensor at a driven setpoint frequency to cause saidsensor to intermittently contact a sample to be imaged;

[0018] generating displacement signals in response to oscillations ofsaid sensor;

[0019] moving the sample relative to said sensor to maintain theseparation distance between said sensor and sample; and

[0020] rastering said sensor over the sample surface, wherein saiddriven setpoint frequency is generally equal to the frequency at thepeak of the frequency versus displacement curve of said sensor.

[0021] The present invention provides advantages in that soft samplescan be imaged on a microscopic level using a highly damped sensor whilereducing the shear forces applied to the sample as the sample isscanned.

BRIEF DESCRIPTION OF THE DRAWINGS

[0022] An embodiment of the present invention will now be described morefully with reference to the accompanying drawings in which:

[0023]FIG. 1 is a schematic block diagram of an interfacial forcemicroscope under force-feedback control configured to operate in anintermittent contact mode;

[0024]FIG. 2 is another schematic block diagram of the interfacial forcemicroscope of FIG. 1 showing further detail;

[0025]FIG. 3 is yet another schematic block diagram of the interfacialforce microscope of FIG. 1 showing further detail;

[0026]FIG. 4 is an enlarged, exploded perspective view of adifferential-capacitance displacement sensor forming part of theinterfacial force microscope of FIG. 1;

[0027]FIG. 5 is a schematic block diagram of a force-feedback controllerforming part of the interfacial force microscope of FIG. 1;

[0028]FIG. 6 is a block circuit diagram of a PID controller forming partof the force-feedback controller of FIG. 5;

[0029]FIG. 7 shows a 1 kHz intermittent contact image of Kevlarfiber-epoxy taken using the interfacial force microscope of FIG. 1;

[0030]FIG. 8 shows another 1kHz intermittent contact image of Kevlarfiber-epoxy taken using the interfacial force microscope of FIG. 1highlighting a damaged area; and

[0031]FIG. 9 shows graphs illustrating the magnitude and phase of therelationship between the ratio of V_(demod) and V_(aux) as a function offrequency when the differential-capacitance displacement sensor isoperated in air;

[0032]FIG. 10 shows graphs illustrating the magnitude and phase of therelationship between the ratio of V_(PID) and V_(aux) as a function offrequency when the differential-capacitance displacement sensor isoperated in air;

[0033]FIG. 11 shows graphs illustrating the magnitude and phase of therelationship between the open loop gain GOL as a function of frequencywhen the differential-capacitance displacement sensor is operated in airwith the curves of FIG. 8 superimposed thereon; and

[0034]FIG. 12 shows intermittent contact images of the surfaces ofHexadecane (3.34 cP) and Glycerol (1490 cP).

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

[0035] Referring now to FIG. 1, an interfacial force microscope (IFM)under force-feedback control and configured to operate in anintermittent contact mode to generate microscopic images of a sampleunder observation in accordance with the present invention is shown andis generally indicated to by reference numeral 20. As can be seen, theIFM 20 includes a differential-capacitance displacement (DCD) sensor 22to contact intermittently the sample to be imaged. A controller 24 iscoupled to the DCD sensor 22 as well as to a piezoelectric scanner 26positioned adjacent the DCD sensor 22 and supporting the sample. Thepiezoelectric scanner 26 is responsive to the controller 24 to move thesample in a vertical direction to alter the sensor-sample separation.The piezoelectric scanner 26 is also actuable to move the samplelaterally in an x-y plane to raster the DCD sensor 22 over the sample ata rate equal to about 2 to 3 μm/s. An imager 27 such as a NanoScope IIIaMultiMode manufactured by Digital Instruments receives output from thecontroller 24 and generates surface images of the sample. The controller24 drives the DCD sensor 22 such that it operates in an intermittentcontact mode while maintaining a high quality factor Q. The qualityfactor Q is of a value to achieve sufficient sensor output displacementsignal contrast between out of contact and contact conditions of the DCDsensor 22 and the sample even though the DCD sensor is highly damped inair. Further details of the IFM 20 and in particular, the force-feedbackcontrol will now be described.

[0036]FIGS. 2 and 3 better illustrate the IFM 20. As can be seen, thecontroller 24 includes a force-feedback (FFB) controller 24 a and animage feedback (IFB) controller 24 b. FFB controller 24 a is responsiblefor driving the DCD sensor 22 and includes a feedback circuit tuned toestablish a well defined peak within the displacement-frequency spectrumof the DCD sensor 22 sufficient to achieve the desired high qualityfactor Q. The IFB controller 24 b is responsible for servoing thevertical extension of the piezoelectric scanner 26 to control thesensor-sample separation at each x,y coordinate of the sample beingintermittently contacted by the DCD sensor 22. The FFB controller 24 bis connected to the DCD sensor 22 directly as well as through apreamplifier 28. The preamplifier 28 has a high input impedance toinhibit excessive loading on the DCD sensor 22.

[0037] An amplitude and phase detector 30, a function generator 32, anoscillator 34 and optionally a volt meter 36 are also connected to theFFB controller 24 a. The IFB controller 24 b is connected to theamplitude and phase detector 30 and provides output to thepiezo-controller 26 a of the piezoelectric scanner 26. Thepiezocontroller 26 a in turn drives the piezoelectric tube 26 b of thepiezoelectric scanner in the z-direction to alter the sensor-sampleseparation.

[0038] A multi-channel analog to digital converter (ADC) 44 is connectedto the IFB controller 24 b, the FFB controller 24 a and the amplitudeand phase detector 30. The ADC provides the output to the imager 27. Anoptional oscilloscope 46 is connected to the FFB and IFB controllers 24a and 24 b respectively.

[0039] Turning to FIGS. 2 to 4, the DCD sensor 22 is better illustrated.As can be seen, the DCD sensor 22 includes a stainless steel orBeryllium-Copper (BeCu) common plate 50. A common plate 52 having a pairof torsion bars 54 extending in opposite directions from its sides isdefined by a cut 56 in the common plate 50. The common plate 52 isdisposed above a pair of gold or chromium electrodes 58 mounted on aquartz substrate 60. A tip 62 is attached to the common plate 52 by wayof a conductive adhesive to help to reduce the mass of the DCD sensor22. The tip 62 is fashioned from a wire having a diameter equal to about0.125mm by electrochemical etching and has a parabolic profile. Thecommon plate 52 is connected to the input of the preamplifier 28.

[0040] The electrodes 58 are dc biased and are driven by RF drivingsignals output by the FFB controller 24 a. The RF driving signals are180 degrees out of phase and have a frequency well beyond the mechanicalbandwidth of the DCD sensor 22 (i.e. 1 MHz) to establish an RFcapacitance bridge defined by the electrodes 58 and common plate 52 thatis sensitive to changes in capacitance at an aF level. The electrodes 58are also driven by an AC setpoint signal generally in the range of fromabout 1 kHz to 1.5 kHz which causes the common plate 52 to oscillate aswill be described. The frequency of the AC setpoint signal is a functionof the mechanical properties of the DCD sensor material, its dimensionsetc.

[0041] When the tip 62 encounters the sample supported by thepiezoelectric scanner 26, a force is applied to the tip 62 resulting intorque being applied to the common plate 52. The applied torque causesthe common plate 52 to rotate. Rotation of the common plate 52 changesthe capacitance between the electrodes 58 and the common plate 52 and isdetected by the RF capacitance bridge. When the common plate 52 rotatesby a small angle θ≈δL where δ is the change in the average gap betweenthe common plate 52 and one of the electrodes 58 and L is the distancebetween the mid-point of the torsion bar axis and the tip 62, adisplacement signal appears on the common plate 52. The displacementsignal has an amplitude equal to 2ΔCV_(ac)/C_(Total), where ΔC is thechange in capacitance, V_(ac) is the amplitude of the RF driving signalsand C_(Total) is equal to two times the capacitance between the commonplate 52 and one electrode 58 plus any stray capacitance in parallelwith the DCD sensor 22. The displacement signal has a frequency equal tothe frequency of the RF driving signals and a phase dependent on thedirection of rotation of the common plate 52. The displacement signal onthe common plate 52 is picked up by the preamplifier 28, amplified andconveyed to the FFB controller 24 a.

[0042]FIG. 5 better illustrates the FFB controller 24 a. As is shown,FFB controller 24 a includes a demodulator 70 receiving the displacementsignal output of the preamplifier 28 and the RF signal output of thefunction generator 32. The demodulator 70 demodulates and low passfilters the displacement signal output of the preamplifier 28 togenerate demodulator amplitude signal output V_(demod). The demodulatorsignal output V_(demod) is applied to the amplitude and phase detector30 and to a PID controller 72. The PID controller 72 also receives theAC setpoint signal output of the oscillator 34 and generates V_(PID) and−V_(PID) feedback signals. The −V_(PID) feedback signal is conveyed toone of the channels of ADC 44 and to the oscilloscope 46 while theV_(PID) feedback signal is conveyed to an RF PID controller 74. The RFPID controller 74 also receives a DC voltage and the RF signal output ofthe function generator 32 from the demodulator 70 and supplies the RFdriving signals to each of the electrodes 58.

[0043] The PID controller 72 is better illustrated in FIG. 6 and as canbe seen, it includes a summing amplifier 80 having unity gain. Thesumming amplifier receives the demodulator signal output V_(demod) aswell as the AC setpoint signal V_(aux) from oscillator 34. The sumoutput of the summing amplifier 80 is therefore −(V_(aux)+V_(demod)) andrepresents the error signal for the DCD sensor feedback loop. The sumoutput of the amplifier 80 is applied to aproportional-integral-derivative (PID) control block 82. The PID controlblock 82 has a good low frequency response and provides outputproportional to the combination of its input, the time integral of itsinput and the time rate of change of its input. The output of the PIDcontrol block 82 is conveyed to a pair of summing amplifiers 84 and 86functioning as high-pass filters, one amplifier 84 of which generatesthe V_(PID) feedback signal and the other amplifier 86 of whichgenerates the −V_(PID) feedback signal. Since the summing amplifier 80has unity gain, the gain G_(PID) from the input of the PID control block82 to the output of the summing amplifier 84 can be expressed as:

G _(PID)=−(G _(P) +G _(I) +G _(D))

[0044] where:

[0045] G_(P) is the proportional gain and is equal to −1;

[0046] G_(I) is the integrator gain and is equal to j/wT_(I);

[0047] G_(D) is the derivative gain and is equal to G_(D) =−Γ[jωT_(D)/(1+jωT _(D))] over the frequency range of interest;

[0048] T_(I) is the time constant of the integrator;

[0049] T_(D) is the time constant of the differentiator; and

[0050] Γ represents the gain at the end of the high-pass filter circuit.

[0051] The gain term G_(PID) allows the frequency response of the DCDsensor feedback loop to be tailored.

[0052] If the frequency of the AC setpoint signal V_(aux) is near dc,the setpoint signal V_(aux) acts as the driven setpoint of the DCDsensor causing the DCD sensor 22 to oscillate physically such that theresulting feedback signal V_(demod) output by demodulator 70 cancels thesetpoint signal V_(aux). In this case, the resulting error signal−(V_(aux)+V_(demod)) is basically equal to zero. When the AC setpointsignal V_(aux) is moved to higher frequencies, the feedback system isunable to offset the AC setpoint signal V_(aux) resulting in errorsignals which can be quite large.

[0053] Prior to imaging, the electronic gains of the integrator anddifferentiator of the PID controller 72 are adjusted such that thesensor displacement signal is nearly in-phase with the AC setpointsignal V_(aux) at the frequency where the open loop gain falls to one(1). In other words, the feedback system has very little phase marginbefore it becomes unstable. However, the feedback system exhibits a muchhigher quality factor Q then if operated without feedback. The PIDcontroller gain adjustments are chosen to obtain a quality factor Q highenough to be sensitive to perturbations caused by the tip striking thesample but not so large that noise becomes an issue. Noise becomes anissue when the quality factor Q is increased to a point where the phasemargin becomes so small that the feedback system edges too close to thebrink of instability.

[0054] Once tuning of the PID controller 72 has been completed, thedisplacement vs. frequency plot of the DCD sensor 22 is examined to findthe frequency of maximum displacement. The frequency of the setpointsignal V_(aux) is then set to the frequency of maximum displacement sothat the DCD sensor 22 oscillates at this frequency. At this time, thepiezoelectric scanner 26 is actuated to bring the sample towards the DCDsensor 22 so that the tip 62 intermittently contacts the sample as thecommon plate 52 oscillates. When the tip 62 contacts the sample, theamplitude of the DCD displacement signal decreases.

[0055] The amplitude and phase detector 30 applies the amplitude signalV_(demod) to the IFB controller 24 b which in turn outputs a magnitudesignal to the piezo-controller 26 a controlling the piezoelectric tube26 b . The imaging set point is set about 3% lower than the initialoutput of the amplitude and phase detector 30. The piezoelectric scanner26 in turn moves the sample towards the DCD sensor 22 to control theseparation between the tip 62 and the sample such that the displacementsignal of the DCD sensor 22 is constant but lower than the in-air case.During this process, the piezoelectric scanner 26 is rastered in an x-yplane to image the surface of the sample under observation.

[0056] The error signals of the piezoelectric scanner feedback loop areapplied to the ADC 44 which also receives phase input from the amplitudeand phase detector 30 and the V_(PID) feedback signal from the FFBcontroller 24 a. The digital output of the ADC 44 is conveyed to theimager 27 to allow images to be formed. The error signals of thepiezoelectric scanner feedback loop provide edge-contrast information ofthe sample surface topography while the phase of the displacement signalprovides information related to energy dissipation during tip and samplecontact.

[0057] By keeping the mass of the DCD sensor 22 low and establishing awell defined peak in V_(demod), a high quality factor is maintained.This allows the DCD sensor to be operated in an intermittent contactmode while ensuring sufficient contrast between out of contact andcontact displacement signals generated by the DCD sensor. As a result,high quality images of the sample under observation can be generated ata microscopic level.

[0058] For a test sample, a fiber composite comprised of Kevlar 49fibers imbedded in an epoxy matrix (the fiber volume fraction isreported to be 50%) was imaged using the IFM 20. Prior to imaging, thesample was polished. FIG. 7 shows a 1 kHz intermittent contact IFM image(all images: 180×180 points, plane subtraction, no filtering) of thefiber composite sample. The ˜50 nm deep polishing grooves are clearlyevident, in spite of a maximum height difference of ˜740 nm. The pieceof debris at the left edge remained undisturbed by the imagingprocedure. The total imaging time was 11 min, corresponding to 20contact cycles per point.

[0059]FIG. 8 shows a 1 kHz intermittent contact IFM image of a badlydamaged area on the Kevlar sample. The massive surface upheaval resultsin a maximum height difference approaching 3 μm, which deaccentuates theshallow polishing grooves in the unblemished fiber regions. In spite ofthe upheaval, the intermittent contact mode technique had littledifficulty in tracking the surface topography, although optimum imagingrequired doubling the number of contact cycles per point.

[0060] To determine the peak contact force during imaging, theseparation between the tip 62 and a single Kevlar 49 fiber was narroweduntil the first evidence of intermittent contact was observed, and thenthe piezoelectric tube 26 b was advanced until the set point wasreached. After dividing the amplitude and phase detector output by theappropriate gain terms, it was estimated that the oscillation amplitudeof the common plate 52 was reduced from 18.97 nm in air to 18.36 nmduring intermittent contact (amplitudes being expressed as peak-to-peakvalues). The distance that the piezoelectric tube 26 b advanced to reachthe set point was 9.9 Å, which is to be compared to the 6.1 Å reductionin the common plate oscillation amplitude.

[0061]FIG. 12 shows intermittent contact images of the surfaces ofHexadecane (3.34 cP) and Glycerol (1490 cP). As will be appreciated, theDCD sensor 22 can be controlled under force-feedback to image soft aswell as hard samples.

[0062] In the intermittent contact mode, the motion of the common plate52 decays only during the contact portion of the cycle. Therefore, thedifference between the advancement of the piezoelectric tube 26 b andthe reduction in common plate oscillation amplitude is a reasonableestimate of the maximum tip-sample deformation, which is about 3.8 Å.

[0063] To estimate the peak contact force, the Hertz equation forelastic contact which is appropriate for axis symmetric parabolic bodiesis used: $F = {\frac{4}{3}E*\sqrt{R}*D^{3/2}}$

[0064] where:

R=(1/R _(t)+1/R _(s))⁻¹

[0065] E^(*) = [(1 − v_(t)²)/E_(t) + (1 − v_(s)²)/E_(s)]⁻¹

[0066] and is the reduced modulus;

[0067] D is the combined deformation of the tip and sample;

[0068] v_(t), v_(s) refer to Poisson's ratio;

[0069] E_(t), E_(s) indicate Young's modulus;

[0070] R_(t), R_(s) represent parabolic radii of curvature; and

[0071] t, s denote tip and sample.

[0072] To test the sensor feedback loop, the ratio V_(demod)/V_(aux),and the ratio V_(PID)/V_(aux)) as a function of frequency were measuredwith the DCD sensor 22 operating in air. It is easy to show thattheoretically V_(demod)/V_(aux)=G_(OL)/(1−G_(OL)) andV_(PID)/V_(aux)=G_(PID)/(1−G_(OL)), whereG_(OL)=−G_(PID)G_(force)G_(mech)G_(bridge)G_(preamp)G_(demod) is theopen loop gain, the minus sign being a result of the summing amplifier80. FIGS. 9 and 10 show how these two ratios vary with frequency whenthe DCD sensor 22 operates under the following set of conditions:

T1=4.3×10⁻⁵ s; T _(D)=3.6×10⁻⁵ s; Γ=2.4; and G _(demod)=4.1

[0073] G_(demod) is referenced to the peak-to-peak amplitude of thepreamplifier output. The solid line passing through the experimentalpoints is the theoretical result. The level of agreement between theoryand experiment ranges from good to excellent.

[0074] Of note in the magnitude plots is the presence of thewell-defined peak occurring around 660 Hz signifying that the sensorfeedback loop behaves much like a second-order low-pass filter. Theorigin of this behavior is rooted in Barkhausen's criterion for feedbackstability. In other words, the term 1/(1−G_(OL)) tends to infinity ifthe magnitude of G_(OL) approaches unity and the corresponding phaseapproaches zero.

[0075]FIG. 11 shows the calculated frequency dependence of G_(OL) withthe magnitude plot for V_(demod)/V_(aux) superimposed. As can be seen,the magnitude of G_(OL) is roughly 0 dB (or 1) and the correspondingphase is about 0.08Π at the peak frequency for demodulator output signalV_(demod). The phase margin is small enough to obtain a strong resonanceresponse, but large enough to prevent the sensor feedback loop fromgoing into self-oscillation. It is important to note that a peak in thedemodulator output signal V_(demod) does not mean mechanical resonance.In the example shown, the peak frequency for the demodulator outputsignal V_(demod) is in fact 60 Hz lower than ω₀/2Π, the mechanicalresonant frequency of the DCD sensor 22. Nevertheless, a maximum in thedemodulator output signal V_(demod) does mean a maximum in thedisplacement amplitude, but this is not achieved in the usual way.Looking at the magnitude plot for V_(PID)/V_(aux), it can be seen thatthe applied force varies over the frequency range, and reaches a maximumin the vicinity of the peak frequency for the demodulator output signalV_(demod).

[0076] A comparison between the phase plots shows that the phase of thedisplacement (or V_(demod)) lags the phase of the force (or V_(PID)) byan angle reasonably close to Π/2. This, along with the fact that a 60 Hzdifference in frequency is not very large, suggests that ω₀ does play animportant role in obtaining a strong peak, which can be understood inthe following way. In order to obtain a strong peak and still maintainfeedback stability, one must make G₁ the dominant electronic gain termbecause it is the only electronic gain that rolls off its response withincreasing frequency, which means that the phase lag due to theelectronics is not far removed from Π/2 over the frequency range ofinterest. The mechanical phase lag eventually reaches Π/2 at ω₀, whichyields an overall phase lag in the neighborhood of the Π phase lagrequired to bring the phase of G_(OL) to zero.

[0077] As will be appreciated, the present invention provides advantagesin that samples can be imaged on a microscopic level without damagingthe samples. This makes the present imaging technique particularlysuited to imaging soft samples including emulsions and liquids. Imagescan be taken for several hours without removing the varying dc offset inthe force signal which is required during contact mode imaging to ensureminimal contact force between the tip and the sample.

[0078] Although the present invention has been described with specificreference to interfacial force microscopy and use of adifferential-capacitance displacement sensor, those of skill in the artwill appreciate that the feedback control used in the preset imagingtechnique can be used with other heavily-damped displacement sensors. Itwill also be appreciated by those of skill in the art, that variationsand modifications may be made to the present invention without departingfrom the spirit and scope thereof as defined by the appended claims.

We claim:
 1. An apparatus for intermittent contact imaging comprising: asensor to contact intermittently a sample to be imaged and generatingdisplacement signals during oscillation thereof; a scanner adjacent saidsensor and supporting said sample to be imaged, said scanner beingactuable to move said sample relative to said sensor to bring saidsensor into intermittent contact with said sample; and a controller incommunication with said sensor and said scanner, said controllerincluding a sensor feedback circuit receiving said displacement signalsand an AC setpoint signal, said AC setpoint signal having a frequencygenerally equal to the frequency at the peak of the displacement versusfrequency curve of said sensor, the output of said sensor feedbackcircuit being applied to said sensor to oscillate the same, saidcontroller further providing output to said scanner in response to saiddisplacement signals to control the separation distance between saidsensor and said sample.
 2. An apparatus as defined in claim 1 whereinsaid sensor feedback circuit is adjusted such that said displacementsignals are generally in-phase with said AC setpoint signal at thefrequency where the open loop gain of said sensor feedback circuit fallsgenerally to one.
 3. An apparatus as defined in claim 2 wherein saidsensor feedback circuit includes a summing junction summing said ACsetpoint signal and said displacement signals, a control block having agood low frequency response receiving the output of said summingjunction and generating feedback signals and a high-pass junction tosupply said feedback signals to said sensor.
 4. An apparatus as definedin claim 3 wherein said summing junction is constituted by a summingamplifier and wherein said control block is aproportional-integral-derivative controller.
 5. An apparatus as definedin claim 4 wherein during adjustment of said sensor feedback circuit,electronic gains of the integrator and differentiator of saidproportional-integral-derivative controller are adjusted.
 6. Anapparatus as defined in claim 5 wherein oscillations of said sensor aredetected by an RF capacitance bridge established at said sensor, saidcapacitance bridge generating said displacement signals.
 7. An apparatusas defined in claim 6 wherein said sensor includes a common platesupported by oppositely extending torsion bars above a pair ofelectrodes and carrying a tip to contact said sample, said electrodesbeing driven by high frequency signals to establish said RF capacitancebridge and being driven by said feedback signals to cause said commonplate to oscillate.
 8. An apparatus as defined in claim 7 wherein saidtip is secured to said common plate by conductive adhesive and has agenerally parabolic configuration.
 9. An apparatus as defined in claim 4further including a demodulator to demodulate and low pass filter saiddisplacement signals before said displacement signals are conveyed tosaid summing amplifier.
 10. An apparatus as defined in claim 9 furtherincluding a preamplifier disposed between said sensor and saiddemodulator.
 11. An apparatus as defined in claim 10 further includingan amplitude and phase detector and an image feedback controller, saidamplitude and phase detector receiving the output of said demodulatorand providing output signals to said image feedback controller, saidimage feedback controller being responsive to said amplitude and phasedetector and controlling the actuation of said scanner to maintain theoscillation displacement of said sensor generally at a constant.
 12. Anapparatus as defined in claim 11 further including an analog to digitalconverter receiving said feedback signals, phase signals from saidamplitude and phase detector and error signals from a scanner feedbackcircuit and providing output to an imager, said imager generating imagesof said sample in response to said signals.
 13. An apparatus as definedin claim 2 wherein the frequency of said AC setpoint signal has afrequency equal to the frequency at the peak.
 14. An apparatus asdefined in claim 13 wherein said feedback circuit behaves similar to asecond-order, low-pass filter.
 15. An interfacial force microscopecomprising: a differential-capacitance displacement sensor having a tipmounted on an oscillating member, said sensor generating displacementsignals during oscillation of said member; a scanner adjacent saidsensor and supporting a sample to be imaged, said scanner being actuableto move said sample relative to said sensor to bring said tip intointermittent contact with said sample and to move said sample relativeto said sensor to raster said sensor over said sample; and a controllerin communication with said sensor and said scanner, said controllerincluding a sensor feedback circuit receiving said displacement signalsand an AC setpoint signal, said AC setpoint signal having a frequencygenerally equal to the frequency at the peak of the displacement versusfrequency curve of said sensor, the output of said sensor feedbackcircuit being applied to said sensor to oscillate the same, saidcontroller further providing output to said scanner in response to saiddisplacement signals to control the separation distance between saidsensor and said sample.
 16. An interfacial force microscope as definedin claim 15 wherein said sensor feedback circuit is adjusted such thatsaid displacement signals are generally in-phase with said AC setpointsignal at the frequency where the open loop gain of said sensor feedbackcircuit falls generally to one.
 17. An interfacial force microscope asdefined in claim 16 wherein said displacement sensor includes a commonplate supported by oppositely extending torsion bars above a pair ofelectrodes and carrying a tip to contact said sample, said electrodesbeing driven by high frequency signals to establish said RF capacitancebridge and being driven by said feedback signals to cause said commonplate to oscillate, said RF capacitance bridge detecting changes incapacitance between said common plate and electrodes and generating saiddisplacement signals.
 18. An interfacial force microscope as defined inclaim 17 wherein said feedback circuit sums said low frequency signaland said displacement signal to generate an error signal, said errorsignal being used to generate the feedback signals to cancel rotationaltendencies of said common plate.
 19. An interfacial force microscope asdefined in claim 18 wherein said sensor feedback circuit includes asumming junction summing said low frequency signal and said displacementsignal, a control block having a good low frequency response receivingthe output of said summing junction and generating said feedback signalsand a high-pass junction to supply said feedback signals to said sensor.20. An apparatus as defined in claim 19 wherein during adjustment ofsaid sensor feedback circuit, electronic gains of the integrator anddifferentiator of said proportioned-integral-derivative controller areadjusted.
 21. An interfacial force microscope as defined in claim 15wherein the frequency of said AC setpoint signal has a frequency equalto the frequency at the peak.
 22. An interfacial force microscope asdefined in claim 21 wherein said feedback circuit behaves similar to asecond-order, low-pass filter.
 23. A method of imaging a sample surfacecomprising the steps of: oscillating a sensor at a driven setpointfrequency to cause said sensor to intermittently contact a sample to beimaged; generating displacement signals in response to oscillations ofsaid sensor; moving the sample relative to said sensor to maintain theseparation distance between said sensor and sample; and rastering saidsensor over the sample surface, wherein said driven setpoint frequencyis generally equal to the frequency at the peak of the frequency versusdisplacement curve of said sensor.